We show that the word problem is decidable for an amalgamated free product of finite inverse\ud
semigroups (in the category of inverse semigroups). This is in contrast to a recent result of M. Sapir\ud
that shows that the word problem for amalgamated free products of finite semigroups (in the category\ud
of semigroups) is in general undecidable
Abstract. Given a word w over a finite alphabet Σ and a finite deterministic automaton A = Q, Σ, δ , the inequality |δ(Q, w)| ≤ |Q| − n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. The word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.